By Professor Donald Brown, Professor Felix Kubler (auth.)
This monograph provides a normal equilibrium technique for microeconomic coverage research. it's meant to function an alternative choice to the now classical, axiomatic normal equilibrium conception as exposited in Debreu`s thought of price (1959) or Arrow and Hahn`s common aggressive research (1971).
The method proposed during this monograph doesn't presume the life of marketplace equilibrium, accepts the inherent indeterminancy of nonparametric basic equlibrium types, and provides potent algorithms for computing counterfactual equilibria in those versions. It contains numerous essays written during the last decade, a few with colleagues or former graduate scholars, and an appendix through Charles Steinhorn at the components of O-minimal constructions, the mathematical framework for our analysis.
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Extra info for Computational Aspects of General Equilibrium Theory: Refutable Theories of Value
Then by the standard duality arguments given above, V rationalizes (pr /I r , xr ), r = 1, . . , N where I r = pr · xr for each r, in the sense that if −V (p, I) > −V (pr , I r ) then p · xr > I. Equivalently, if −V (p/I, 1) > −V (pr /I r , 1) then xr · (p/I) > 1 = xr · (pr /I r ) for r = 1, . . , N . Then applying Chiappori and Rochet’s result to −V and interchanging the roles of p and x implies that there exist numbers V j , γ j > 0, j = 1, . . , N such that for all i = j, V i − V j > −γ j xj · pi pj − j i I I (i, j = 1, .
An economy in which individual endowments are collinear, is not subtle. If we do not observe the individual endowments 3 Recent work by Chiappori and Ekeland [CE98] considers a related question. They show that observations of aggregate endowments and prices place no restrictions on the local structure of the equilibrium manifold. Uniqueness, Stability, and Comparative Statics 29 and only observe prices and income levels, then one set of individual endowments consistent with this data is collinear, with shares given by the observed income distribution.
Brown and Chris Shannon Using this terminology, we can restate the question above: given a ﬁnite data set, when does there exist a nonsatiated utility function which rationalizes these observations? The classic answer to this question was given by Afriat [Afr67]. Theorem (Afriat). The following are equivalent: (a) There exists a nonsatiated utility function which rationalizes the data. (b) The data satisﬁes Cyclical Consistency. , N ). (d) There exists a concave, monotone, continuous, nonsatiated utility function which rationalizes the data.